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Publications Influence

Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

- V. Batyrev
- Mathematics
- 1 October 1993

We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials… Expand

1,006 123- PDF

Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

- V. Batyrev, D. Straten
- Mathematics, Physics
- 30 July 1993

We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV1,...,Vr in a toric… Expand

338 32- PDF

New Trends in Algebraic Geometry: Birational Calabi–Yau n -folds have equal Betti numbers

- V. Batyrev
- Mathematics
- 16 October 1997

Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local number… Expand

136 22- PDF

Tamagawa numbers of polarized algebraic varieties

- V. Batyrev, Y. Tschinkel
- Mathematics
- 1 December 1997

Let ${\cal L} = (L, \| \cdot \|_v)$ be an ample metrized invertible sheaf on a smooth quasi-projective algebraic variety $V$ defined over a number field. Denote by $N(V,{\cal L},B)$ the number of… Expand

91 22- PDF

On the Hodge structure of projective hypersurfaces in toric varieties

- V. Batyrev, D. Cox
- Mathematics
- 25 June 1993

This paper generalizes classical results of Griffiths, Dolgachev and Steenbrink on the cohomology of hypersurfaces in weighted projective spaces. Given a $d$-dimensional projective simplicial toric… Expand

187 19- PDF

Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs

- V. Batyrev
- Mathematics, Physics
- 16 March 1998

Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural Kawamata… Expand

172 18- PDF

Stringy Hodge numbers of varieties with Gorenstein canonical singularities

- V. Batyrev
- Mathematics, Physics
- 6 November 1997

We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic variety X with at worst log-terminal singularities. We prove some basic properties of stringy E-functions… Expand

178 17- PDF

Mirror duality and string-theoretic Hodge numbers

- V. Batyrev, L. Borisov
- Mathematics, Physics
- 1 October 1995

Abstract. We prove in full generality the mirror duality conjecture for string-theoretic Hodge numbers of Calabi–Yau complete intersections in Gorenstein toric Fano varieties. The proof is based on… Expand

169 16- PDF

Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry

- V. Batyrev, D. Dais
- Mathematics, Physics
- 4 October 1994

Abstract We propose a new higher dimensional version of the McKay correspondence which enables us to understand the “Hodge numbers” assigned to singular Gorenstein varieties by physicists. Our… Expand

204 16- PDF